Diffusion for chaotic plane sections of 3-periodic surfaces

• 成果类型: Article
• 署名作者: Avila, Artur; Hubert, Pascal; Skripchenko, Alexandra
• 署名单位: Universite Paris Cite; Aix-Marseille Universite; HSE University (National Research University Higher School of Economics)
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-016-0650-z
• 发表日期: 2016
• 页码: 109-146
• 关键词: interval exchange transformations; teichmuller flow; moduli space; pseudogroups; simplicity; uniqueness; formalism; deviation; EXISTENCE; DYNAMICS

摘要

We study chaotic plane sections of some particular family of triply periodic surfaces. The question about possible behavior of such sections was posed by S. P. Novikov. We prove some estimations on the diffusion rate of these sections using the connection between Novikov's problem and systems of isometries-some natural generalization of interval exchange transformations. Using thermodynamical formalism, we construct an invariant measure for systems of isometries of a special class called the Rauzy gasket, and investigate the main properties of the Lyapunov spectrum of the corresponding suspension flow.